2018 AIME II Problem 6

A real number a is chosen randomly and uniformly from the interval [-20,18]. The probability that the roots of the polynomial

x^{4}+2 a x^{3}+(2 a-2) x^{2}+(-4 a+3) x-2

are all real can be written in the form \frac{m}{n}, where m and n are relatively prime positive integers. Find m+n.